That's not an Identity!

If \(x\) and \(y\) are positive integers, and satisfy

\[(x+y)!=x!+y!\]

Find \(x\) and \(y\). Enter \(x+y\) as your answer.

\[\]Notation: \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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